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Simplifying (2c + -5)(c + -6) + (c + 6)(3c + -2) = 0 Reorder the terms: (-5 + 2c)(c + -6) + (c + 6)(3c + -2) = 0 Reorder the terms: (-5 + 2c)(-6 + c) + (c + 6)(3c + -2) = 0 Multiply (-5 + 2c) * (-6 + c) (-5(-6 + c) + 2c * (-6 + c)) + (c + 6)(3c + -2) = 0 ((-6 * -5 + c * -5) + 2c * (-6 + c)) + (c + 6)(3c + -2) = 0 ((30 + -5c) + 2c * (-6 + c)) + (c + 6)(3c + -2) = 0 (30 + -5c + (-6 * 2c + c * 2c)) + (c + 6)(3c + -2) = 0 (30 + -5c + (-12c + 2c2)) + (c + 6)(3c + -2) = 0 Combine like terms: -5c + -12c = -17c (30 + -17c + 2c2) + (c + 6)(3c + -2) = 0 Reorder the terms: 30 + -17c + 2c2 + (6 + c)(3c + -2) = 0 Reorder the terms: 30 + -17c + 2c2 + (6 + c)(-2 + 3c) = 0 Multiply (6 + c) * (-2 + 3c) 30 + -17c + 2c2 + (6(-2 + 3c) + c(-2 + 3c)) = 0 30 + -17c + 2c2 + ((-2 * 6 + 3c * 6) + c(-2 + 3c)) = 0 30 + -17c + 2c2 + ((-12 + 18c) + c(-2 + 3c)) = 0 30 + -17c + 2c2 + (-12 + 18c + (-2 * c + 3c * c)) = 0 30 + -17c + 2c2 + (-12 + 18c + (-2c + 3c2)) = 0 Combine like terms: 18c + -2c = 16c 30 + -17c + 2c2 + (-12 + 16c + 3c2) = 0 Reorder the terms: 30 + -12 + -17c + 16c + 2c2 + 3c2 = 0 Combine like terms: 30 + -12 = 18 18 + -17c + 16c + 2c2 + 3c2 = 0 Combine like terms: -17c + 16c = -1c 18 + -1c + 2c2 + 3c2 = 0 Combine like terms: 2c2 + 3c2 = 5c2 18 + -1c + 5c2 = 0 Solving 18 + -1c + 5c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + -0.2c + c2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -0.2c + -3.6 + c2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -0.2c + c2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -0.2c + c2 = 0 + -3.6 -0.2c + c2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -0.2c + c2 = -3.6 The c term is -0.2c. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2c + 0.01 + c2 = -3.6 + 0.01 Reorder the terms: 0.01 + -0.2c + c2 = -3.6 + 0.01 Combine like terms: -3.6 + 0.01 = -3.59 0.01 + -0.2c + c2 = -3.59 Factor a perfect square on the left side: (c + -0.1)(c + -0.1) = -3.59 Can't calculate square root of the right side. The solution to this equation could not be determined.
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